We can solve this problem using the future value of an annuity formula, because Jack and Jill need to know how much to deposit each year to reach a specific amount in 18 years. Here's how we break it down:

1. Future Value Needed:
   Jack and Jill need to accumulate enough for 1 year of tuition 18 years from now, which is $\$150,000$.

2. Annual Interest Rate:
   The couple is expected to earn a 6% return on their investment annually.

3. Number of Years:
   They have 18 years to accumulate the funds.

The Future Value of an Annuity Formula:

$FV = P \times \frac{(1 + r)^n - 1}{r}$

Where:

• $FV$ is the future value (the amount they need in the future, $150,000).
• $P$ is the annual payment (this is what we're solving for).
• $r$ is the annual interest rate (6% or 0.06).
• $n$ is the number of years (18 years).

Rearrange the formula to solve for $P$: $P = \frac{FV \times r}{(1 + r)^n - 1}$

Now, substitute the values:

• $FV = 150,000$
• $r = 0.06$
• $n = 18$

$P = \frac{150,000 \times 0.06}{(1 + 0.06)^{18} - 1}$

Let's calculate this next.The couple should begin depositing approximately $4,853.48 annually at the end of each year to accumulate enough funds for one year of college tuition 18 years from now, assuming a 6% annual rate of return.

Would you like further details or have any other questions?

Here are 5 related questions for further exploration:

1. How much would they need to deposit annually if tuition were expected to be $200,000 per year?
2. How does changing the interest rate to 5% affect the annual deposit required?
3. What if they want to save for 4 years of tuition instead of just 1 year?
4. How much would they need to deposit monthly instead of annually?
5. What if they started saving 10 years before college instead of 18?

Tip: When investing, compound interest plays a significant role over time, so starting early can reduce the required annual deposit.